Thread: Linear Algebra please help.

T:R2-->R3 defined by T(a1,a2)=(a1+a2,0,2a1-a2)

I need to prove that is a linear transformation, and find the bases for both
N(T) and R(T). then compute the nullity and rank of T. finally say where it is one -2- one or onto.

I already got the anwsers but I need to know in detail especially for computing the nullity and rank of T. and onto or one 2 one.
Thanks

Originally Posted by JCIR

T:R2-->R3 defined by T(a1,a2)=(a1+a2,0,2a1-a2)

I need to prove that is a linear transformation

Its just checking rules right? Do it.

Or get a matrix that represents the transformation.

and find the bases for both

Consider the standard base for .

Now

So the basis for .

N(T) and R(T). then compute the nullity and rank of T. finally say where it is one -2- one or onto.

N(T) is .This means Nullity = 0

R(T) is .

This means R(T) will be the subspace of R3, in which the second co-ordinate is 0.This means Rank = 2.

The map is one-one because nullity is 0.